4.DETAILSa) What is the expected value of X? 2The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is:f(x,^) = λ e-^x for 0 ≤ x ≤ ∞, λ = 0.5. is what R calls rate.Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for theexponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts.b) What is the variance of X? 4c) What is the standard deviation of X? 2Enter a number.d) What is the probability that X is greater than its expected value?e) What is the probability that X is > 5?f) What is the probability that X is > 10?g) What is the probability that X > 10 given that X > 5?h) What is the median of X?1) Enter any comments in the text box below.Submit AnswerMY NOTESViewing Saved Work Revert to Last ResponseASK YOUR TEACHER

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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d) What is the probability that X is greater than its expected value? e) What is the probability that X is> 5? f) What is the probability that X is> 10? |